Suarez noted it's his first save at any level -- in the Minors or at home in Venezuela.
He didn't think he'd pitch in the ninth until manager Bruce Bochy dispatched him to the plate in the eighth.
"That was my thought, 'OK, I'm going to hit. OK, I'm going to the ninth,'" said Suarez, who clocked 95 mph on his fastball during the outing. "It's my mentality to always do my job."
In an otherwise lackluster season, Suarez's help in the bullpen since being recalled July 22 has been encouraging. The Giants, too, hope Suarez can continue to be the team's swingman -- someone who can easily go two or three innings to patch up a game, or perhaps make a spot start.
Bochy noted he hasn't had a true swingman since Yusmeiro Petit pitched for San Francisco from 2013-15.
"He's a nice swingman," Bochy said of Suarez. "... He's tough on lefties and righties. This should help his confidence. He's missed a lot of time, along with the other guys."
The soft-spoken Suarez, who hurt his calf while rehabbing his shoulder this season in the Minors, has impressed many, including Giants pitcher Jeff Samardzija. Suarez helped protect Samardzija's third consecutive win.
"He has a great personality. He never complains and he always wants to pitch," Samardzija said. "He's a big boy, as you can see. He's always ready to pitch, that's for sure."
Asked how his first save felt, Suarez said: "It's even better when it's a strikeout," referring to his K of Chris Iannetta to end the game.
Suarez would like to start a game at some point before the clock strikes midnight on this season, like he did last season. But the right-hander said he's open to anything, really. It's part of why the Giants are so excited about Suarez's future.
"I just go there every day to be ready to pitch," Suarez said. "No matter where. I prepare myself to be out there every day until the last out. Any way I can help the team, I just do it."